Complicated Error Structure Research Articles

Trellis plots as visual aids for analyzing split plot experiments

ABSTRACTThe analysis of split plot experiments can be challenging due to a complicated error structure resulting from restrictions on complete randomization. Similarly, standard visualization methods do not provide the insight practitioners desire to understand the data, think of explanations, generate hypotheses, build models, or decide on next steps. This article demonstrates the effective use of trellis plots in the preliminary data analysis for split plot experiments to address this problem. Trellis displays help to visualize multivariate data by allowing for conditioning in a general way. They can also be used after the statistical analysis for verification, clarification, and communication.

Animal movement constraints improve resource selection inference in the presence of telemetry error.

Multiple factors complicate the analysis of animal telemetry location data. Recent advancements address issues such as temporal autocorrelation and telemetry measurement error, but additional challenges remain. Difficulties introduced by complicated error structures or barriers to animal movement can weaken inference. We propose an approach for obtaining resource selection inference from animal location data that accounts for complicated error structures, movement constraints, and temporally autocorrelated observations. We specify a model for telemetry data observed with error conditional on unobserved true locations that reflects prior knowledge about constraints in the animal movement process. The observed telemetry data are modeled using a flexible distribution that accommodates extreme errors and complicated error structures. Although constraints to movement are often viewed as a nuisance, we use constraints to simultaneously estimate and account for telemetry error. We apply the model to simulated data, showing that it outperforms common ad hoc approaches used when confronted with measurement error and movement constraints. We then apply our framework to an Argos satellite telemetry data set on harbor seals (Phoca vitulina) in the Gulf of Alaska, a species that is constrained to move within the marine environment and adjacent coastlines.

Error distributions on large entangled states with non-Markovian dynamics.

We investigate the distribution of errors on a computationally useful entangled state generated via the repeated emission from an emitter undergoing strongly non-Markovian evolution. For emitter-environment coupling of pure-dephasing form, we show that the probability that a particular patten of errors occurs has a bound of Markovian form, and thus, accuracy threshold theorems based on Markovian models should be just as effective. Beyond the pure-dephasing assumption, though complicated error structures can arise, they can still be qualitatively bounded by a Markovian error model.

Fast dimension-reduced climate model calibration and the effect of data aggregation

How will the climate system respond to anthropogenic forcings? One approach to this question relies on climate model projections. Current climate projections are considerably uncertain. Characterizing and, if possible, reducing this uncertainty is an area of ongoing research. We consider the problem of making projections of the North Atlantic meridional overturning circulation (AMOC). Uncertainties about climate model parameters play a key role in uncertainties in AMOC projections. When the observational data and the climate model output are high-dimensional spatial data sets, the data are typically aggregated due to computational constraints. The effects of aggregation are unclear because statistically rigorous approaches for model parameter inference have been infeasible for high-resolution data. Here we develop a flexible and computationally efficient approach using principal components and basis expansions to study the effect of spatial data aggregation on parametric and projection uncertainties. Our Bayesian reduced-dimensional calibration approach allows us to study the effect of complicated error structures and data-model discrepancies on our ability to learn about climate model parameters from high-dimensional data. Considering high-dimensional spatial observations reduces the effect of deep uncertainty associated with prior specifications for the data-model discrepancy. Also, using the unaggregated data results in sharper projections based on our climate model. Our computationally efficient approach may be widely applicable to a variety of high-dimensional computer model calibration problems.

Correlated measurement error hampers association network inference.

Modern chromatography-based metabolomics measurements generate large amounts of data in the form of abundances of metabolites. An increasingly popular way of representing and analyzing such data is by means of association networks. Ideally, such a network can be interpreted in terms of the underlying biology. A property of chromatography-based metabolomics data is that the measurement error structure is complex: apart from the usual (random) instrumental error there is also correlated measurement error. This is intrinsic to the way the samples are prepared and the analyses are performed and cannot be avoided. The impact of correlated measurement errors on (partial) correlation networks can be large and is not always predictable. The interplay between relative amounts of uncorrelated measurement error, correlated measurement error and biological variation defines this impact. Using chromatography-based time-resolved lipidomics data obtained from a human intervention study we show how partial correlation based association networks are influenced by correlated measurement error. We show how the effect of correlated measurement error on partial correlations is different for direct and indirect associations. For direct associations the correlated measurement error usually has no negative effect on the results, while for indirect associations, depending on the relative size of the correlated measurement error, results can become unreliable. The aim of this paper is to generate awareness of the existence of correlated measurement errors and their influence on association networks. Time series lipidomics data is used for this purpose, as it makes it possible to visually distinguish the correlated measurement error from a biological response. Underestimating the phenomenon of correlated measurement error will result in the suggestion of biologically meaningful results that in reality rest solely on complicated error structures. Using proper experimental designs that allow for the quantification of the size of correlated and uncorrelated errors, can help to identify suspicious connections in association networks constructed from (partial) correlations.

Radar for hydrology: Unfulfilled promise or unrecognized potential?

Hydrology requires accurate and reliable rainfall input. Because of the strong spatial and temporal variability of precipitation, estimation of spatially distributed rain rates is challenging. Despite the fact that weather radars provide high-resolution (but indirect) observations of precipitation, they are not used in hydrological applications as extensively as one could expect. The goal of the present review paper is to investigate this question and to provide a clear view of the opportunities (e.g., for flash floods, urban hydrology, rainfall spatial extremes) the limitations (e.g., complicated error structure, need for adjustment) and the challenges for the use of weather radar in hydrology (i.e., validation studies, precipitation forecasting, mountainous precipitation, error propagation in hydrological models).

Development of a curved ray tracing method for modeling of phase paths from GPS radio occultation: A two‐dimensional study

A two‐dimensional curved ray tracer (CRT) is developed to study the propagation path of radio signals across a heterogeneous planetary atmosphere. The method, designed to achieve improvements in both computational efficiency and accuracy over conventional straight‐line methods, takes rays' first‐order bending into account to better describe curved raypaths in the stratified atmosphere. CRT is then used to simulate the phase path from GPS radio occultation (RO). The merit of the ray tracing approach in GPS RO is explicit consideration of horizontal variation in the atmosphere, which may lead to a sizable error but is disregarded in traditional retrieval schemes. In addition, direct modeling of the phase path takes advantage of simple error characteristics in the measurement. With provision of ionospheric and neutral atmospheric refractive indices, in this effort, rays are traced along the full range of GPS‐low Earth orbiting (LEO) radio links just as the measurements are made in real life. Here, ray shooting is employed to realize the observed radio links with controlled accuracy. CRT largely reproduces the very measured characteristics of GPS signals. When compared, the measured and simulated phases show remarkable agreement. The cross validation between CRT and GPS RO has confirmed not only the strength of CRT but also the high accuracy of GPS RO measurements. The primary motivation for this study is enabling effective quality control for GPS RO data, overcoming a complicated error structure in the high‐level data. CRT has also shown a great deal of potential for improved utilization of GPS RO data for geophysical research.

Models of tree-level hollow incidence in Victorian State forests

This paper details predictive models of tree-level hollow incidence for State forests in central and eastern Victoria. Models are based on the hollows component of the Statewide Forest Resource Inventory (SFRI), the most comprehensive database of hollow incidence in Australia. A two-stage methodology was used at the individual tree-level that in its first-stage generated a statement of the probability of hollows presence, and in its second-stage estimated the size of hollows. The hierarchical nature of SFRI data prompted the search for statistical methodology capable of explicitly modelling a complicated error structure. Subsequently, generalised linear mixed models (GLMMs) were used to estimate first-stage, tree-level models in the presence of spatial and nested dependence. The developed models were statistically and biologically plausible and performed well when validated using independent data. By overcoming the limitations facing previous research associated with insufficient data and inappropriate statistical methodology viable predictive models were developed. Tree-level models will help us understand patterns of hollow incidence, can be used for predictive purposes when individual-tree information is available, and can improve habitat tree retention guidelines.

Biomarker Discovery for Arsenic Exposure Using Functional Data. Analysis and Feature Learning of Mass Spectrometry Proteomic Data

Plasma biomarkers of exposure to environmental contaminants play an important role in early detection of disease. The emerging field of proteomics presents an attractive opportunity for candidate biomarker discovery, as it simultaneously measures and analyzes a large number of proteins. This article presents a case study for measuring arsenic concentrations in a population residing in an As-endemic region of Bangladesh using plasma protein expressions measured by SELDI-TOF mass spectrometry. We analyze the data using a unified statistical method based on functional learning to preprocess mass spectra and extract mass spectrometry (MS) features and to associate the selected MS features with arsenic exposure measurements. The task is challenging due to several factors, the high dimensionality of mass spectrometry data, complicated error structures, and a multiple comparison problem. We use nonparametric functional regression techniques for MS modeling, peak detection based on the significant zero-downcrossing method, and peak alignment using a warping algorithm. Our results show significant associations of arsenic exposure to either under- or overexpressions of 20 proteins.

Observable trend-projecting state-space models

Much attention has focused in recent years on the use of state-space models for describing and forecasting industrial time series. However, several state-space models that are proposed for such data series are not observable and do not have a unique representation, particularly in situations where the data history suggests marked seasonal trends. This raises major practical difficulties since it becomes necessary to impose one or more constraints and this implies a complicated error structure on the model. The purpose of this paper is to demonstrate that state-space models are useful for describing time series data for forecasting purposes and that there are trend-projecting state-space components that can be combined to provide observable state-space representations for specified data series. This result is particularly useful for seasonal or pseudo-seasonal time series. A well-known data series is examined in some detail and several observable state-space models are suggested and compared favourably with the constrained observable model.